A Level Maths Notes: FP1 – Solving Differential Equations - The Integrating Factor Method
Any equation of the form
(1)
might be solved using the integrating factor method. This method
finds a function of
that
the left hand side can be multiplied by so that the left hand side
can be written
The
integral of this is just
so
if we can find a function h(x) we can write the solution down as an
integral which may (or may not) be evaluated. The integrating factor
for (1) is
Multiplying
(1) by
gives
The left hand side can be
written
Integrating both sides now
gives
Now divide both sides by
to
give
Example: Solve the
differential equation
The integrating factor is
Example: Solve the
differential equation
The integrating factor is
Dividing by
If the coefficient of
is
not 1 it must be made 1.
Example: Solve the
differential equation
Divide byto
give
The integrating factor is
